I agree with Eric Page. Ohm's law rules. And generally speaking, a switch should not get warm. If it does, it is either overloaded, defective (high internal resistance), or its external connections have high resistance.
It is OK to use AC rated switches in airplanes. B&C Aero sells AC rated switches. Hundreds of them have been installed in aircraft. Even if the DC rating is not marked on the side of the switch, every switch can carry a certain amount of DC current. Usually switch manufactures will test the DC ampacity of their products and the results are published on their datasheets. When a switch is already closed, it doesn't matter if the current is AC or DC. The issue is what happens when the switch first starts to open (or bounces open while closing). This is where voltage is important. When the contacts of the switch first separate just a hair, an arc jumps across the opening. Since AC current periodically drops to zero, the arc is quickly extinguished. But DC keeps arcing as the contacts spread apart. That arcing damages the contacts. In order to minimize arcing, the DC voltage needs to be reduced. Yes, switches need to be derated when conducting DC. But one way to look at it is that the voltage is derated, not the current. If two identical switches carry equal current, one in a DC circuit and one in an AC circuit, the life expectancy of the switches is equal provided that the DC circuit operates at a reduced voltage. If the AC voltage is 115, a DC voltage of about 28 will result in equal switch life. Most of home-built airplanes have 12 volt electrical systems. At that voltage, a switch can carry more than its 115 VAC current rating, provided that it is snap acting (opens quickly).

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